Table 1.
Parameters Used in the Simulated Calculations of the Integral Weight
Wavelength | Two Subaperture Center-to-Center Distance | Receiving Aperture Diameter | Beacon Diameter |
---|
(nm) | (m) | (m) | (m) |
550 | 0.24 | 0.12 | 0 |
Table 2.
Condition Number at Various Measurement Intervals
Measuring Interval | | | |
Condition number | | | |
Algorithm 1.
CGNR Algorithm
Input: Available (Measured) data , integral weight |
Output: the inversion values |
Given an initial guess |
Compute |
For until convergence Do |
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EndDo |
Algorithm 2.
PCGNR Algorithm
Input: Available (Measured) data , integral weight |
Output: the inversion values |
Given an initial guess , let be a given preconditioner |
Compute |
For until convergence Do |
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EndDo |
Algorithm 3.
Auto Correction Algorithm
Input: Original retrieved profile, , from the PCGNR |
method. |
Output: Corrected retrieved profile, . |
1. Set , correction serial , threshold coefficients |
, weight factors |
; |
2. Initial ; |
3. FOR |
4. compute incre_diff(i); |
5. |
6. END FOR |
7. Compute MeanIncreDiff; |
8. Compute three discriminant thresholds. ; |
9. FOR |
10. IF &&(incre\_diff |
11. Choose as ; |
12. Calculate the corrected value using |
; |
13. ELSE IF && |
&& |
14. Choose as ; |
15: Calculate the corrected value using |
; |
16. ELSE IF&& |
17. Choose as ; |
18. Calculate the corrected value using |
; |
19. Use to replace ; |
20. |
21.END FOR |
22. PRINT ; |
Table 3.
SNRs and RMSEs for the Different Methods at Different Noise Levels (NL) for the HV 5/7 Turbulence Profile
| | | | |
---|
Methods | SNR/RMSE | SNR/RMSE | SNR/RMSE | SNR/RMSE |
---|
Tikhonov | 41.3579/0.1498 | 34.2733/0.3217 | 29.1100/0.5716 | 27.4379/0.6882 |
TSVD | 25.8525/0.8102 | 25.8505/0.8148 | 24.6503/0.9414 | 24.1808/0.9964 |
CGNR | 41.3532/0.1499 | 34.2790/0.3213 | 29.1056/0.5718 | 27.4371/0.6882 |
LSQR | 41.3532/0.1499 | 34.2790/0.3213 | 29.1056/0.5718 | 27.4371/0.6882 |
PCGNR | 48.4593/0.0634 | 39.7831/0.1772 | 33.1702/0.3634 | 30.6145/0.4830 |
Auto-corrected PCGNR | 50.1207/0.0496 | 47.0033/0.0734 | 39.5314/0.1818 | 35.6006/0.2849 |
Table 4.
SNRs and RMSEs for the Different Methods at Different Noise Levels (NL) for the GreenWood Turbulence Profile
| | | | |
---|
Methods | SNR/RMSE | SNR/RMSE | SNR/RMSE | SNR/RMSE |
---|
Tikhonov | 41.6426/0.1473 | 34.2366/0.3305 | 29.3869/0.5661 | 27.4124/0.7059 |
TSVD | 26.5077/0.7753 | 25.7570/0.8456 | 25.2979/0.8916 | 24.5234/0.9808 |
CGNR | 41.6441/0.1472 | 34.2335/0.3306 | 29.3839/0.5665 | 27.4136/0.7058 |
LSQR | 41.6441/0.1472 | 34.2335/0.3306 | 29.3839/0.5665 | 27.4136/0.7058 |
PCGNR | 48.1807/0.0677 | 39.3220/0.1932 | 33.1523/ 0.3702 | 30.8180/0.4831 |
Auto-corrected PCGNR | 49.5442/0.0545 | 45.7132/0.0968 | 39.2509/0.1905 | 35.0526/0.3126 |
Table 5.
SNRs and RMSEs for the Different Methods at Different Noise Levels (NL) for the Hefei Day Turbulence Profile
| | | | |
---|
Methods | SNR/RMSE | SNR/RMSE | SNR/RMSE | SNR/RMSE |
---|
Tikhonov | 34.4302/0.3157 | 33.3400/0.3628 | 29.3852/0.5670 | 27.5614/0.6981 |
TSVD | 25.6479/0.8589 | 25.4772/0.8781 | 24.9758/0.9337 | 24.5860/0.9761 |
CGNR | 34.4266/0.3159 | 33.3379/0.3630 | 29.3876/0.5669 | 27.5626/0.6979 |
LSQR | 34.4266/0.3159 | 33.3379/0.3630 | 29.3876/0.5669 | 27.5626/0.6979 |
PCGNR | 40.5078/0.1597 | 37.9450/0.2193 | 32.9835/0.3784 | 30.5952/0.4970 |
Auto-corrected PCGNR | 44.4076/0.0987 | 43.0361/0.1214 | 38.1499/0.2188 | 34.4338/0.3352 |
Table 6.
SNRs and RMSEs for the Different Methods at Different Noise Levels (NL) for the Hefei Night Turbulence Profile
| | | | |
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Methods | SNR/RMSE | SNR/RMSE | SNR/RMSE | SNR/RMSE |
---|
Tikhonov | 31.3434/0.4614 | 30.9530/0.4841 | 29.2020/0.5962 | 27.6712/0.7082 |
TSVD | 25.4851/0.9027 | 25.4075/0.9126 | 24.7312/1.0041 | 24.0436/1.0845 |
CGNR | 31.3455/0.4613 | 30.9491/0.4843 | 29.1907/0.5970 | 27.6774/0.7076 |
LSQR | 31.3455/0.4613 | 30.9491/0.4843 | 29.1907/0.5970 | 27.6774/0.7076 |
PCGNR | 34.3798/0.3274 | 34.2660/0.3338 | 32.3071/0.4175 | 30.6339/0.5082 |
Auto-corrected PCGNR | 38.6108/0.1982 | 39.2175/0.1867 | 38.1577/0.2144 | 35.6582/0.2920 |
Table 7.
SNRs and RMSEs for the Different Methods at Different Noise Levels (NL) for the Instrumented Balloon Profile (Launched at Noon on 12 November 2015)
| | | | |
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Methods | SNR/RMSE | SNR/RMSE | SNR/RMSE | SNR/RMSE |
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Tikhonov | 27.8201/0.6514 | 27.8806/0.6479 | 27.0160/0.7184 | 26.2119/0.7901 |
TSVD | 26.0813/0.8234 | 26.2467/0.8067 | 24.7819/0.9925 | 23.9132/1.0944 |
CGNR | 27.8160/0.6517 | 27.8812/0.6495 | 27.0152/0.7185 | 26.2141/0.7899 |
LSQR | 27.8160/0.6517 | 27.8812/0.6495 | 27.0152/0.7185 | 26.2141/0.7899 |
PCGNR | 33.5456/0.3429 | 33.3578/0.3499 | 31.4183/0.4377 | 29.5978/0.5421 |
Auto-corrected PCGNR | 37.6441/0.2124 | 37.6325/0.2142 | 34.9531/0.2985 | 32.9086/0.3762 |
Table 8.
SNRs and RMSEs for the Different Methods at Different Noise Levels (NL) for Instrumented Balloon Profile (Launched in the Morning on 14 November 2015)
| | | | |
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Methods | SNR/RMSE | SNR/RMSE | SNR/RMSE | SNR/RMSE |
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Tikhonov | 33.6191/0.3473 | 33.0611/0.3758 | 29.3191/0.5735 | 27.4814/0.7045 |
TSVD | 24.7301/ 0.9582 | 24.6593/0.9700 | 23.6090/1.1121 | 23.0376/1.1853 |
CGNR | 33.6048/0.3482 | 33.0650/0.3756 | 29.3305/0.5726 | 27.4799/0.7046 |
LSQR | 33.6048/0.3482 | 33.0650/0.3756 | 29.3305/0.5726 | 27.4799/0.7046 |
PCGNR | 37.8372/0.2181 | 36.9969/0.2396 | 32.7070/0.3913 | 30.5683/0.4973 |
Auto-corrected PCGNR | 41.7286/0.1359 | 41.2757/0.1432 | 37.4651/0.2315 | 34.5893/0.3191 |